Question

Sin 2x-3 sinx cos x=-1​

Answer 1

Ответ:

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Answer 2

To solve the equation sin(2x) - 3sin(x)cos(x) = -1, we can use some trigonometric identities and manipulation.

First, we'll express sin(2x) in terms of sin(x) and cos(x) using the double-angle identity for sine:

sin(2x) = 2sin(x)cos(x)

Now, substitute this into the original equation:

2sin(x)cos(x) - 3sin(x)cos(x) = -1

Now, factor out sin(x)cos(x):

(2 - 3)sin(x)cos(x) = -1

-sin(x)cos(x) = -1

Now, divide both sides by -1:

sin(x)cos(x) = 1

Next, we can use the double-angle identity for sine again to rewrite sin(x)cos(x) in terms of sine:

sin(2x) = 2sin(x)cos(x)

So,

2sin(x)cos(x) = sin(2x)

Now, our equation becomes:

sin(2x) = 1

To solve for x, take the inverse sine (arcsin) of both sides:

2x = arcsin(1)

arcsin(1) = π/2

Now, divide both sides by 2:

x = π/4

So, the solution to the equation sin(2x) - 3sin(x)cos(x) = -1 is x = π/4.